If you spin the spinner 36 times, what is the best prediction possible for the number of times
it will land on green or blue?

Answer:

5x

6xy

2x3y

hope it's helpful

Answer:

The correct answer is:

10√2

Explanation:

In a right triangle, the hypotenuse is the side opposite the right angle and is also the longest side. The other two sides are called the legs.

In this problem, the hypotenuse of the resulting triangles is given as 20 inches. Since the quilt squares are cut on the diagonal to form triangular quilt pieces, the hypotenuse of each triangle is formed by the diagonal cut of a square.

Let's denote the side length of each square as "s" inches.

According to the Pythagorean Theorem, which relates the sides of a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs.

In this case, the hypotenuse is 20 inches, so we have:

20^2 = s^2 + s^2 (since the two legs of the right triangle are the sides of the square)

400 = 2s^2

Dividing both sides by 2, we get:

200 = s^2

Taking the square root of both sides, we get:

s = √200

Since we are looking for the side length of each piece in simplified radical form, we can further simplify √200 as follows:

√200 = √(100 x 2) = 10√2

So, the side length of each quilt piece is 10√

The side length of each piece of the triangular pieces of quilt cut from squares will be 10√2 inches.

This is a simple mathematics problem that can be solved using the Pythagoras theorem. This theorem states that in a right-angled triangle, the square root of the sum of the two perpendicular sides (p,b) is equal to the longest side, called the hypotenuse (h).

[tex]h = \sqrt{p^2 + b^2}[/tex]

Since the triangle pieces have been cut from a square, they will be right-angled triangles, and the two perpendicular sides will be equal, i.e., p = b.

20 = √2p²  (since p and b are equal, b can be taken as p)

On squaring both sides,

400 = 2p²

p² = 400/2

p² = 200

p = √200

p = 10√2 = b

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The radius of the water bottle which is in cylindrical shape is approximately 2.12 cm.

A cylinder is a three-dimensional shape that consists of two congruent, parallel circular bases that are connected by a curved lateral surface. The lateral surface of the cylinder is formed by a rectangle that is wrapped around the circular bases.

A cylinder can be thought of as a circular prism, where the bases are circles and the lateral surface is curved. The height of a cylinder is the perpendicular distance between the two bases, and the radius is the distance from the center of the base to the edge of the circular base.

The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height. We can rearrange this formula to solve for the radius:

r = √(V/πh)

Substituting the given values, we have:

r = √(150/π(8.9))

r ≈ 2.12 cm (rounded to two decimal places)

Therefore, the radius of the water bottle is approximately 2.12 cm.

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"It can vary - it really depends on the distribution of the variable."

The number of intervals, or bins, to choose when creating a histogram can vary depending on the distribution of the variable.

Most often, about 8-10 intervals are used, but there is no set rule. It is generally recommended to have at least 5 intervals, but if the data is highly skewed or has outliers, more intervals may be needed to accurately represent the distribution.

Ultimately, the goal is to choose a number of intervals that provides a clear visual representation of the data without oversimplifying or overcomplicating the histogram.

The number of intervals or bins to be chosen when creating a histogram can vary and it really depends on the distribution of the variable.

While most often, about 8-10 bins are used, there is no hard and fast rule for the number of bins to be used in a histogram.

In general, the number of bins should be large enough to display the shape of the distribution clearly, but not so large that it obscures important features of the distribution or leads to overfitting.

A minimum of 5 bins is recommended to display the basic shape of the distribution, but more bins may be necessary for complex or multi-modal distributions.

Depending on the distribution of the variable, a histogram's number of intervals or bins can be altered.

There is no established guideline, however 8–10 intervals are typically utilized.

A minimum of five intervals are often advised, however if the data is extremely skewed or contains outliers, more intervals could be required to correctly depict the distribution.

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Compartmentalized is the type of data that is discussed in the problem researched by an employee rylie who is a newly hired cybersecurity expert for a government agency and has working experience in the private sector.

Data classification is the way of organizing data into different categories that make it easy to retrieve, sort and store for future use. In simple words, compartmentalization means to separate into isolated compartments or categories. In data language, A nonhierarchical grouping of information used to control access to data more finely than with hierarchical security classification alone is called Compartmentalization. Now, we have a rylie who is a newly hired cybersecurity expert for a government agency. She has working experience in the private sector. On basis of her experience she has discovered that, the private sector companies often had confusing hierarchies for data classification as compared to the government's classifications which are well known and standardized. During her training, she is researching data that requires special authorization beyond normal classification. The data type that she researched and that is authorization beyond normal classification is called compartmentalized data.

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For all given Quadrilaterals none has enough information provided in the problem to definitively say - if they are a parallelogram.Hence, option E is correct for all.

If a quadrilateral is a parallelogram, it satisfies the following properties:

It is important to note that in order to definitively conclude that a quadrilateral is a parallelogram, all four properties must be satisfied. If only one or some of the properties are met, it does not necessarily guarantee that the quadrilateral is a parallelogram.

Figure 1-: Adjacent angles are 105 and 75 degrees, which satify the condition of opposite angles being equal but except this no other information is provided, Hence, we don't have enough information to say figure 1 is a parallelogram.

Figure 2-: Diagonals bisect each other and make angle 65 degree with each other. Given that Diagonal 1 bisects Diagonal 2 and the opposite sides of the quadrilateral are equal, by using SAS criterion, the congruency of triangles formed by the diagonals can be derived to say that the opposite angles of the quadrilateral are also equal . However, we still need more information about parallelism of sides to definitively say given quadrilateral is a parallelogram.

Figure 3-: One pair of opposite side is equal in length ,while other pair of line is parallel to each other.This information is insufficient to determine if given quadrilateral is a parallelogram.

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The correct statement regarding the null hypothesis is: the null hypothesis claims the opposite of what the researcher believes.

The null hypothesis is the claim that no relationship exists between two sets of data or variables being analyzed. The

null hypothesis is that any experimentally observed difference is due to chance alone, and an underlying causative

relationship does not exist, hence the term "null".

In research, the null hypothesis is a statement of no effect or no relationship between variables, while the alternative

hypothesis represents the effect or relationship the researcher is interested in demonstrating.

The purpose of statistical testing is to determine whether there is enough evidence to reject the null hypothesis in

favor of the alternative hypothesis.

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Answer:

The answer is 28

Step-by-step explanation:

sin0=opp/hyp

let hyp be x

sin30=14/x

0.5x=14

divide both sides by 0.6

x=14/0.5

x=28

Answer:

x = -5, x = 1

As (x, y) coordinates, the x-intercepts are (-5, 0) and (1, 0).

Step-by-step explanation:

The x-intercepts are the x-values of the points at which the curve crosses the x-axis, so when y = 0.

From inspection of the given graph, we can see that the parabola crosses the x-axis at x = -5 and x = 1.

Therefore, the x-intercepts of the parabola are:

As (x, y) coordinates, the x-intercepts are (-5, 0) and (1, 0).

The percentage of the original area of wetlands currently left in the United States is approximately 50%. So, the correct

option is 50% (option 3).

Percentages are a way of expressing a proportion or a fraction as a part of 100. It is denoted by the symbol "%".

According to the United States Environmental Protection Agency (EPA), it is estimated that about 50% of the original

wetlands in the contiguous United States have been lost since the 1600s due to human activities such as agriculture,

development, and urbanization. Therefore, the correct answer to the question is 50%.

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The percentage of the original area of wetlands currently left in the United States is approximately 50%.

Wetlands are regions of land where the soil is continually or intermittently soaked with water. Wetlands have a particular hydrology, soil, and vegetation mix that results in specialised ecosystems that offer a variety of ecological functions.

There are many different types of habitats where wetlands can be found, such as coastal locations, interior regions, and high-altitude mountain regions. They come in a variety of shapes, such as marshes, swamps, bogs, fens, and estuaries, and can be freshwater, brackish, or saline.

Wetlands are significant for several reasons. For species, such as migrating birds, amphibians, and fish, they offer crucial habitats. They also aid in removing contaminants from water, lessen the effects of flooding, and give people access to recreational activities. Wetlands are crucial for carbon sequestration as well.
Based on the information provided, the question is asking for the approximate percentage of the original area of wetlands currently left in the United States. The answer is approximately 50%.

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The probability of the sample mean being less than 79 is 77.64%

In order to solve the given problem we have to take the help of Standard error mean

SEM = ∑/√(n)

here,

∑ = population standard deviation

n = sample size

hence, the z-score can be calculated as

z = ( x' - μ)/σ/√(n)

here,

x' = sample mean

μ = population mean

σ = population standard deviation

n = sample size

adding the values into the formula

SEM = σ / √(n)

= 21/√64

= 2.625

z = (x' - μ)/SEM

= (79-77)/2.625

= 0.76

now, using standard distribution table we find that probability of a z-score is less than 0.77 then converting it into percentage

0.77 x 100

= 77%

The probability of the sample mean being less than 79 is 77.64%

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Answer:

x ≈ 39.5°

Step-by-step explanation:

using the cosine ratio in the right triangle

cos x = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{OP}{NP}[/tex] = [tex]\frac{64}{83}[/tex] , then

x = [tex]cos^{-1}[/tex] ( [tex]\frac{64}{83}[/tex] ) ≈ 39.5° ( to the nearest tenth )

The profit (p) is $7500 generated by selling 1500 units of a certain commodity is given by the function p ( x ) = - 1500 + 12 x - 0.004 x²

To maximize our profit, we must locate the vertex of the parabola represented by this function. The x-value of the vertex indicates the number of units that must be sold to maximize profit.

We may use the formula for the x-coordinate of a parabola's vertex:

x = -b/2a

where a and b represent the coefficients of the quadratic function ax² + bx + c. In this situation, a = -0.004 and b = 12, resulting in:

x = -12 / 2(-0.004) = 1500

This indicates that when 1,500 units are sold, the profit is maximized.

To calculate the greatest profit, enter x = 1500 into the profit function:

P(1500) = -1500 + 12(1500) - 0.004(1500)^2

P(1500) = -1500 + 18000 - 9000

P(1500) = $7500

Therefore, the maximum possible profit is $7,500 and it is generated when 1,500 units are sold.

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To achieve this maximum profit, exactly 1500 units must be sold.

To find the maximum profit and the number of units needed to generate it, we can use the given profit function p(x) = -1500 + 12x - 0.004x^2. We need to find the vertex of the parabola represented by this quadratic function, as the vertex will give us the maximum profit and the corresponding number of units.

Step 1: Identify the coefficients a, b, and c in the quadratic function.
In p(x) = -1500 + 12x - 0.004x^2, the coefficients are:
a = -0.004
b = 12
c = -1500

Step 2: Find the x-coordinate of the vertex using the formula x = -b / (2a).
x = -12 / (2 * -0.004) = -12 / -0.008 = 1500

Step 3: Find the maximum profit by substituting the x-coordinate into the profit function p(x).
p(1500) = -1500 + 12 * 1500 - 0.004 * 1500^2
p(1500) = -1500 + 18000 - 0.004 * 2250000
p(1500) = -1500 + 18000 - 9000
p(1500) = 7500

So, the maximum profit is $7,500, and 1,500 units must be sold to generate it.

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Given statement: The rule of thumb for estimating the time of completion is 1.5 times what you originally think it will be.

Given statement is True.

The reason for this rule of thumb is that tasks often take longer than initially estimated due to unforeseen challenges, dependencies, and other factors that can cause delays.

By estimating the time of completion as 1.5 times the original estimate, you are accounting for these potential delays and allowing for a more realistic timeline.

This rule of thumb is not a hard and fast rule, and there will be cases where tasks take less or more time than 1.5 times the original estimate. However, it can be a helpful guideline for project planning and resource allocation, as it helps to ensure that sufficient time and resources are allocated to complete tasks within a realistic timeframe.

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where t is measured in days, and A(t) represents the amount of flooded land at time t. This function has a B-value of -0.3118.

To model the situation of the flood, we can use an exponential decay function, which represents the decreasing amount of flooded land over time. The function can be written as:

[tex]A(t) = A0 * e^{(-kt)}[/tex]

where A(t) is the amount of flooded land at time t, A0 is the initial amount of flooded land, k is a constant representing the rate of decay, and e is the mathematical constant approximately equal to 2.718.

To determine the value of k, we can use the given information that after 2 days, only 3375 acres of land were under water. Substituting t = 2 and A(t) = 3375 into the equation above, we get:

[tex]3375 = A0 * e^{(-2k)[/tex]

We also know that initially, there were 6000 acres of land under water. Substituting A0 = 6000 into the equation above, we get:

Dividing both sides by 6000, we get:

ln(0.5625) = -2k[tex]ln(0.5625) = -2k[/tex]

Taking the natural logarithm of both sides, we get:

[tex]ln(0.5625) = -2k[/tex]

Solving for k, we get:

[tex]k = -ln(0.5625)/2[/tex]

k ≈ 0.3118

Therefore, the function to model the situation of the flood is:

[tex]A(t) = 6000 * e^{(-0.3118t)}[/tex]

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Answer:  the answer is A. 14.

Step-by-step explanation: In each trial of the reenactment, Scott chooses one card from the stack and records its digit. Based on the given data, a digit of or 1 speaks to a objective scored, and a digit of 2 through 9 speaks to a missed endeavor.

Out of the 5 endeavors per amusement, on the off chance that Scott scores precisely 2 objectives, it implies he missed 3 endeavors. Subsequently, the likelihood of this occasion can be calculated as:

P(exactly 2 objectives) = (0.2)²(0.8)³ = 0.008192

This likelihood can be utilized to discover the anticipated number of diversions in which Scott scores precisely 2 objectives, by duplicating it by the overall number of diversions reenacted:

Anticipated number of recreations = P(exactly 2 objectives) × Add up to number of recreations = 0.008192 × 84 ≈ 0.68

Adjusting to the closest entire number, we get that Scott is anticipated to score precisely 2 objectives in 1 diversion out of the 84 recreated diversions.

Thus, the total surface area of cylinder is found to be 480π sq. cm.

A cylinder's surface area is made up of its two congruent, parallel circular sides added together with its curved surface area. You must determine the Base Area (B) and Curved Surface Area in order to determine the surface area of a cylinder (CSA).

As a result, the base area multiplied by two and the area of a curved surface add up to the surface area or total surface of a cylinder.

Given data:

radius r = 8 cm

Height h = 22 cm

Total surface area of cylinder = 2*area of circle + area of curved cylinder

TSA = 2πr² + 2πrh

TSA = 2π(8)² + 2π(8)(22)

TSA = 2π(64) + 2π(176)

TSA = 128π + 352π

TSA = 480π sq. cm.

Thus, the total surface area of cylinder is found to be 480π sq. cm.

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Complete question-

Find the surface area of the cylinder with radius of 8 cm and height of 22 cm. write the answer in terms of pi and round the answer to the nearest hundredths place.

The correct answer is option B. Translate 1 to the left, scale vertically by 1/2, then reflect over the y-axis.

The process of modifying the shape, location, or features of a graph is often referred to as graph transformation. Graphs are visual representations of mathematical functions or data point connections, often represented on a coordinate plane.

Translations, reflections, rotations, dilations, and other changes to the look of a graph are examples of graph transformations.

For the given problem, Transformation to get the desired result can be carried out as:

Hence, to convert the graph of "y = k(x)" to the graph of "y = -k(x + 1)," the correct sequence of transformations is to translate 1 unit to the left, scale vertically by 1/2, and then reflect across the y-axis, which is option B.

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Recall the equation provided in the pdf:

   (125x ^ 3 * y ^ - 12) ^ (- 2/3) = (y ^ [A])/([B] * x ^ [c])

find A B and C.

The answer will be:

We can solve this problem using the rules of exponents and algebraic manipulation.

Starting with the left-hand side of the equation:

(125x^3 * y^-12)^(-2/3)

Using the rule that (a * b)^c = a^c * b^c, we can rewrite the expression as:

125^(-2/3) * x^(-2) * y^(8)

Simplifying further, we can use the fact that a^(-n) = 1/(a^n) to get:

1/(5^2 * x^2 * y^8/3)

Now, we can see that the denominator on the right-hand side of the equation must be 5^2 * x^2 * y^8/3. To find the numerator, we need to simplify the expression y^A. Comparing exponents, we see that:

y^A = y^(8/3)

Therefore, we need to find a value of A such that A = 8/3. Solving for A, we get:

A = 8/3

Now, we can write the equation as:

y^(8/3)/(5^2 * x^2 * y^8/3) = y^(8/3)/(25 * x^2 * y^(8/3))

Comparing exponents again, we see that we need to find values of B and C such that:

B * C = 2

and

-8/3 = -C

Solving for C, we get:

C = 8/3

Substituting this value of C into the first equation, we get:

B * 8/3 = 2

Solving for B, we get:

B = 3/4

Therefore, the solution is:

A = 8/3

B = 3/4

C = 8/3

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The surface area of the two solids are listed below:

Case 1 - 232 square centimeters

Case 2 - 240 square centimeters

The surface area of a solid is the sum of the areas of all its faces. There are two cases of solids whose surface areas must be determined. The area formulas for triangle and rectangle are, respectively:

Triangle

A = 0.5 · b · h

Rectangle

A = b · h

Case 1

A = (6 cm) · (8 cm) + 2 · 0.5 · (6 cm) · (12 cm) + 2 · 0.5 · (8 cm) · (14 cm)

A = 232 cm²

Case 2

A = 2 · 0.5 · (8 cm) · (3 cm) + (8 cm) · (12 cm) + 2 · (5 cm) · (12 cm)

A = 24 cm² + 96 cm² + 120 cm²

A = 240 cm²

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The estimated regression equation for the given data is y = -30.7 + 3.409x

To develop an estimated regression equation for the given data, we need to use the method of least squares.

The formula for the slope of the regression line is given by:

b = ∑(xi - x)(yi - y) / ∑(xi - x)²

where xi and yi are the individual values of the two variables, x and y are their respective means.

The formula for the intercept of the regression line is given by:

a = y - b × x

where a is the intercept and b is the slope.

Using the given data, we can calculate the values of x, y, b, and a as follows

x = (6 + 11 + 15 + 18 + 20) / 5 = 14

y = (7 + 9 + 12 + 21 + 30) / 5 = 15.8

∑(xi - x)(yi - y) = (6 - 14)(7 - 15.8) + (11 - 14)(9 - 15.8) + (15 - 14)(12 - 15.8) + (18 - 14)(21 - 15.8) + (20 - 14)(30 - 15.8) = 306.8

∑(xi - x)² = (6 - 14)² + (11 - 14)² + (15 - 14)² + (18 - 14)² + (20 - 14)² = 90

b = ∑(xi - x)(yi - y) / ∑(xi - x)² = 306.8 / 90 = 3.409

a = y - b × x = 15.8 - 3.409 × 14 = -30.7

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The given question is incomplete, the complete question is:

Given are data for two variables, x and y. Develop an estimated regression equation for these data.

The coin makes approximately 16.53 turns when rolled on its edge for 1.34 m.

The circumference of the coin can be calculated as follows to determine the number of turns it makes:

C = πd

where C is the circumference, d is the diameter, and π is the mathematical constant pi (approximately equal to 3.14159).

So, for the given $2 coin with a diameter of 25.75 mm, the circumference is:

C = πd = 3.14159 x 25.75 mm ≈ 80.926 mm

Divide the distance traveled by the coin's circumference to determine the number of turns it makes when rolled on its edge for 1.34 meter:

Number of turns = distance traveled / circumference of the coin

Number of turns = 1.34 m / 0.080926 m

Number of turns ≈ 16.53

Therefore, the coin makes approximately 16.53 turns when rolled on its edge for 1.34 m.

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After 5 and a half minutes, the temperature of the water will be 77°F.

In this scenario, we are given that the initial temperature of the water is 80°F. We also know that the temperature of the water decreases by 0.5°F every minute. We want to find out what the temperature of the water will be after 5 and a half minutes.

To solve this problem, we need to use a bit of math. We know that the temperature of the water is decreasing by 0.5°F every minute. So after 1 minute, the temperature of the water will be 80°F - 0.5°F = 79.5°F. After 2 minutes, the temperature will be 79.5°F - 0.5°F = 79°F. We can continue this pattern to find the temperature after 5 and a half minutes.

After 5 minutes, the temperature of the water will be 80°F - (0.5°F x 5) = 77.5°F. And after another half minute (or 0.5 minutes), the temperature will decrease by another 0.5°F, so the temperature will be 77.5°F - 0.5°F = 77°F.

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Number of red counters in the original bag is 3, and the number of green counters is 7.

Let's use algebra to solve the problem. Let U be the number of red counters and G be the number of green counters originally in the bag.

From the first part of the problem, we know that

Probability (selecting a green counter) = G / (U + G) = 3/7

Solving for U in terms of G, we get

U = (7G - 3G) / 3 = 4G/3

So we know that there were 4G/3 red counters and G green counters in the bag originally. But since the number of counters must be a whole number, we can assume that there were 4R red counters and 3G green counters originally, where R and G are both integers and R + G is the total number of counters.

After adding 2 red and 3 green counters, the number of counters in the bag is now R + 2 + G + 3 = R + G + 5.

From the second part of the problem, we know that

P(selecting a green counter) = (G + 3) / (R + G + 5) = 6/13

Solving for R in terms of G, we get

R = (13G - 9G - 15) / 7 = 4G/7 - 15/7

Since R must be an integer, we can try different values of G to see if R is an integer. For example, if G = 7, then R = 3 and the total number of counters is 10.

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The given question is incomplete, the complete question is:

There are only U red counters and G green counters in a bag. A counter is taken at random from the bag. The probability that the counter is green is 3/7. The counter is put back in the bag. 2 more red counters and 3 more green counters are put in the bag. A counter is taken at random from the bag. The probability that the counter is green is 6/13. Find the number of red counters and the number of green counters that were in the bag originally

Step-by-step explanation:

rotate the triangle in your mind (or as actual picture on your phone or computer), so that the right angle is the bottom right or bottom left, and C being the opposite bottom angle.

then we see

28 = cos(C) × 35

21 = sin(C) × 35

and so,

sin(C) = 21/35 = 3/5

cos(C) = 28/35 = 4/5

tan(C) = sin(C)/cos(C) = 3/5 / 4/5 = 3/4

For a percentage data of students who play the different game and win the prize, the expected amount to pay for prizes for that booth by the carnival committee is equals to the $218.70.

We have a booth of school carnival in past years, The percentage of students win a stuffed toy = 22%

The percentage of students win a jump rope = 16%

The percentage of students win a t-shirt

= 6%

The winning amount for stuffed toy game = $ 3.60

The winning amount for jump rope game = $1.20

The winning amount for t-shirt game

= $7.90

The remaining students do not win a prize. Now, total number of students play the game at the booth = 150

So, number of students who win stuffed toy = 22% of 150 = 33

Number of students who win jump rope = 16% of 150 = 24

Number of students who win stuffed toy

= 6% of 150 = 9

For determining the expected pay using the simple multiplication formula. Total expected pay for prizes for that booth is equals to the sum of resultant of multiplcation of number of students who play a particular game into pay amount for that game. That is total excepted pay in dollars = 3.60 × 33 + 1.20 × 24 +7.90 × 6

= 218.7

Hence required value is $218.70.

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Answer:

f(x) is the blue graph, g(x) is the red graph.

x^2 - 3x + 17 - (2x^2 - 3x + 1) = 16 - x^2

16 - x^2 = 0 when x = -4, 4

So the area between these two graphs is (using the TI-83 graphing calculator):

fnInt (16 - x^2, x, -4, 4) = 85 1/3

Testing is only one part of the overall assessment process.

What is evaluation in education?

Assessment is an ongoing process of gathering evidence of what each student actually knows, understands, and can do. A comprehensive evaluation approach includes a combination of formal and informal evaluation (formative, preliminary, and summative).

What is an assessment? Also what does it mean?

At the course level, assessments provide important data on the breadth and depth of student learning. Evaluation is more than scoring. It's about measuring student learning progress. Assessment is therefore defined as “the process of data gathering to better understand the strengths and weaknesses of a student's learning”. 

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Answer:

[tex]h(x)=2x^2-12x+9[/tex],  [tex]p(x)=-5x^2-20x-5[/tex]

Step-by-step explanation:

To get to the standard form of a quadratic equation, we need to expand and simplify. Recall that standard form is written like so:

[tex]ax^2+bx+c[/tex]

Where a, b, and c are constants.

Let's expand and simplify h(x).

[tex]2(x-3)^2-9=\\2(x^2+9-6x)-9=\\2x^2+18-12x-9=\\2x^2+9-12x=\\2x^2-12x+9[/tex]

Thus, [tex]h(x)=2x^2-12x+9[/tex]

Let's do the same for p(x).

[tex]-5(x+2)^2+15=\\-5(x^2+4+4x)+15=\\-5x^2-20-20x+15=\\-5x^2-5-20x=\\-5x^2-20x-5[/tex]

Thus, [tex]p(x)=-5x^2-20x-5[/tex]